A note on subvarieties of powers of OT-manifolds
Complex Variables
2024-08-16 v1 Algebraic Geometry
Logic
Abstract
It is shown that the space of finite-to-finite holomorphic correspondences on an OT-manifold is discrete. When the OT-manifold has no proper infinite complex-analytic subsets, it then follows by known model-theoretic results that its cartesian powers have no interesting complex-analytic families of subvarieties. The methods of proof, which are similar to [Moosa, Moraru, and Toma ``An essentially saturated surface not of K\"ahler-type", {\em Bull. of the LMS}, 40(5):845--854, 2008], require studying finite unramified covers of OT-manifolds.
Cite
@article{arxiv.2408.08049,
title = {A note on subvarieties of powers of OT-manifolds},
author = {Rahim Moosa and Matei Toma},
journal= {arXiv preprint arXiv:2408.08049},
year = {2024}
}
Comments
The paper is published